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Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. A ... More


Knowing: The Nature of Physical Law

Michael Munowitz

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195167375
eISBN:
9780199787104
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195167375.001.0001
Subject:
Physics, History of Physics

This book interprets the book of nature for curious readers of all sorts, but especially for those looking to appreciate the power and beauty of physics without having to grapple with the ... More


Intertheoretic Relations—Mechanics

Robert W. Batterman

in The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195146479
eISBN:
9780199833078
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195146476.003.0007
Subject:
Philosophy, Philosophy of Science

This chapter discusses limiting correspondence relations between quantum mechanics and classical mechanics. The semiclassical limit is singular and no reductive relation obtains between these two ... More


Hamilton–Jacobi Theory

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0019
Subject:
Physics, Atomic, Laser, and Optical Physics

The Hamilton-Jacobi theory is the apotheosis of Lagrangian and Hamiltonian mechanics: action functions encode all of the possible trajectories of a mechanical system satisfying certain criteria. ... More


Three-Part Invention

Michael Munowitz

in Knowing: The Nature of Physical Law

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195167375
eISBN:
9780199787104
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195167375.003.0004
Subject:
Physics, History of Physics

The Moon — caught in an exact balance of attractive and repulsive forces — orbits the Earth with flawless regularity, never faltering. A ball rolls predictably down a slope of a certain grade, always ... More


PATH INTEGRALS IN PHASE SPACE

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter contains a few additional results such as a definition of path integrals over phase space trajectories, and the problems generated by the quantization of lagrangians with potentials ... More


Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Alfonso Sorrentino

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.001.0001
Subject:
Mathematics, Applied Mathematics

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ... More


Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Vadim Kaloshin and Ke Zhang

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was ... More


Classical Mechanics

Jeffrey A. Barrett

in The Conceptual Foundations of Quantum Mechanics

Published in print:
2019
Published Online:
July 2020
ISBN:
9780198844686
eISBN:
9780191889196
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198844686.003.0001
Subject:
Philosophy, Philosophy of Science

While quantum mechanics is one of the most successful physical theories we have ever had, it is deeply counterintuitive. It must be given the empirical evidence it explains. We consider some of the ... More


The problem of polyatomic molecules

CARLO CERCIGNANI

in Ludwig Boltzmann: The Man Who Trusted Atoms

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198570646
eISBN:
9780191717949
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570646.003.0008
Subject:
Physics, History of Physics

Polyatomic molecules created difficulties in kinetic theory from the start, with the problem of thermal capacities or specific heats. If the problem of specific heats was initially solved with the ... More


Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Published in print:
2011
Published Online:
December 2013
ISBN:
9780191001628
eISBN:
9780191775161
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780191001628.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics, and of the relation of classical mechanics to relativity and quantum theory. A ... More


Theories in History and Practice

Steven French

in There Are No Such Things As Theories

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198848158
eISBN:
9780191882715
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198848158.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

This eliminativist view must immediately face the concern that scientists themselves appear to be committed to the existence of theories. They talk about them, apparently refer to them, argue that ... More


What is this Book About?

M. Suhail Zubairy

in Quantum Mechanics for Beginners: with applications to quantum communication and quantum computing

Published in print:
2020
Published Online:
June 2020
ISBN:
9780198854227
eISBN:
9780191888649
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198854227.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter begins with a brief history of how classical mechanics evolved into quantum mechanics. Next a bird’s-eye view of the basic aspects of quantum mechanics and its applications is given. In ... More


Classical Mechanics

Jill North

in Physics, Structure, and Reality

Published in print:
2021
Published Online:
June 2021
ISBN:
9780192894106
eISBN:
9780191915239
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192894106.003.0004
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

This chapter applies our reasoning about structure in physics to two formulations of classical mechanics, Lagrangian and Newtonian mechanics, that are generally taken to be completely equivalent. It ... More


Lagrangian and Hamiltonian Dynamics

Peter Mann

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book explores the fascinating subject of classical mechanics, which is the pinnacle of nineteenth-century physics, from a fresh and exciting viewpoint. With its foundations laid down in ancient ... More


Classical Mechanics According to Newton and Hamilton

Jochen Autschbach

in Quantum Theory for Chemical Applications: From Basic Concepts to Advanced Topics

Published in print:
2020
Published Online:
February 2021
ISBN:
9780190920807
eISBN:
9780197508350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190920807.003.0002
Subject:
Chemistry, Quantum and Theoretical Chemistry

This chapter introduces classical mechanics, starting with the familiar definitions of position, momentum, velocity, acceleration force, kinetic, potential, and total energy. It is shown how the ... More


Newton, Laplace, and Determinism

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses a few of the central, but sometimes unspoken, scientific ideas or assumptions about the world. It first looks at the character of Newtonian physics and classical mechanics by ... More


The Classical Connection

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0015
Subject:
Mathematics, Applied Mathematics

This chapter discusses the relationship between the elegance of the classical Lagrangian and Hamiltonian formulations of mechanics and optics. In physics, action is a mathematical functional which ... More


Classical Covariance

Moataz H. Emam

in Covariant Physics: From Classical Mechanics to General Relativity and Beyond

Published in print:
2021
Published Online:
May 2021
ISBN:
9780198864899
eISBN:
9780191897313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198864899.003.0003
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

Classical mechanics, from point particles through rigid objects and continuum mechanics is reviewed based on the notions of tensors, transformations, and the metric, as developed in the first two ... More


Introduction

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0001
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

The introduction gives the plan of the book and guides the reader to the main points. The book is divided into four parts: Part I provides a complete derivation of the entropy of the ideal gas, a ... More


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